A new simple asymmetric hysteresis operator and its application to inverse control of piezoelectric actuators

Piezoelectric actuators (PEAs) are commonly used as micropositioning devices due to their high resolution, high stiffness, and fast frequency response. Because piezoceramic materials are ferroelectric, they fundamentally exhibit hysteresis behavior in their response to an applied electric field. The positioning precision can be significantly reduced due to nonlinear hysteresis effects when PEAs are used in relatively long-range applications. This paper describes a new, precise, and simple asymmetric hysteresis operator dedicated to PEAs. The complex hysteretic transfer characteristic has been considered in a purely phenomenological way, without taking into account the underlying physics. This operator is based on two curves. The first curve corresponds to the main ascending branch and is modeled by the function f₁. The second curve corresponds to the main reversal branch and is modeled by the function g₂. The functions f₁ and g% are two very simple hyperbola functions with only three parameters. Particular ascending and reversal branches are deduced from appropriate translations of f₁ and g₂. The efficiency and precision of the proposed approach is demonstrated, in practice, by a real-time inverse feed-forward controller for piezoelectric actuators. Advantages and drawbacks of the proposed approach compared with classical hysteresis operators are discussed.